Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.
Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature or—in modern mathematics—entities that are stipulated to have certain properties, called axioms. A proof consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration.Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent from any scientific experimentation. Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics), but often later find practical applications. The problem of integer factorization, for example, which goes back to Euclid in 300 BC, had no practical application before its use in the RSA cryptosystem, now widely used for the security of computer networks.
Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements. Since its beginning, mathematics was essentially divided into geometry and arithmetic (the manipulation of natural numbers and fractions), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new areas. Since then, the interaction between mathematical innovations and scientific discoveries has led to a rapid lockstep increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method, which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than 60 first-level areas of mathematics.
I'm an ordinary college student who likes physics, engineering mathematics, and electromagnetism. I'm not sure because it's my first time participating in an overseas forum, not a domestic one, but I look forward to your kind cooperation.
I learned to speak several languages other than English but, speaking math wasn't one of them; as soon as numbers and symbols are part of a task, my brain seems to revert to using fingers and toes.
I'm trying to pace myself to get up to speed with my calc and physics before going back to college. It's been so long that I don't know how much we got up to in calc I. Can someone tell me what chapter in Thomas Calculus does calc I go up to, or do they cover the whole thing?
How did you find PF?: Years ago online forums were more visible. These days they are left behind social media. I searched Google and now I am here.
Why in heat transfer books Fourier's partial differtial unsteady state heat transfer equation is solved with seperation of variables but not with...
Let’s say that we know, with 95% confidence, that something is likely to occur when the Universe is between 1058 and 10549 years old.
What is the statistical likelihood that it has already occurred in the first 13.8 billion years of the Universe’s existence? (1.38 X 1010 years)
I know the...
One possible end to the Universe is called vacuum decay, where a Higgs boson could transition from a false vacuum to a true vacuum state. This would create a vacuum decay bubble (known as bubble nucleation) that would expand at light speed, destroying everything in its path.
According to Anders...
Howdy from West Virginia!! If you would have told me 30 years ago that I'd be researching physics and math for fun, I would have said, "Are you high.... and by the way, what is physics?!?" I'm obsessed with all things science, and tickled by all things quantum. I became interested in science and...
Hello, I am currently working on an idea for a possible future masters or PhD in cellular biology, however my idea is currently just a passion project. For it to work, I would need to learn how to predict and make a specific protein to do a specific function, in this instance I need to use it to...
I am a math PhD working in software/technology who is a physics hobbyist. I’ve gone through MIT 8.01 - 8.05 courses and watched and worked through a number of additional videos and problems. My interest is mostly getting exposure to more ideas through the community. I don’t plan on trying to...
Fascinating, and utterly unintuitive.
This is a question that appeared on the American SAT test until it was recently removed. (citation: Veritasium, to which I will not link at this time.)
Every student ever has gotten it wrong, and that's because the SAT writers got it wrong too. The...
I do not know much about this, please help.
My truck seat back cushion is 2" thick. Truck A is ~5,700 lbs from google. 2011 f-150 super cab 6.5ft bed.
Truck B is ~5775. 2015 GMC Yukon xl slt.
If truck A is stopped and braked and truck B hits truck A going 45-55mph creating a force of...
Feynman lectures question where he explains math in terms of nuts.
Feynman has a few lectures where he explained math numbers with Mayan counting as an example.
I am not looking for that example. The example
I am looking for is where he just uses nuts to give examples of math, add...
"Former math teacher explains why some students are good at math and others lag behind"
The title of a news article shown on todays Yahoo site,
https://www.yahoo.com/news/former-math-teacher-explains-why-122744193.html
Looking in the section called "
Why are some students ‘good’ at math and...
If I reason this as follows, I run into problems. Please help me understand what is wrong with reasoning like this.
a) I start with the left hand side of the equation and let that x be -2.
b) I square it. This gives me 4. So I now have the square root of 4.
c) The square root of 4 is +/- 2. The...
okay so I'm a Electrician I've found short method of calculating the final magnitude of a system (Lₜ), this relies mainly on Eucliud's axiom of angles within parrallel lines and is this
∑(cos(θₙ-θₜ)⋅Lₙ)=Lₜ
where Lₙ and θₙ are the initail manignitude and angles respectively, and θₜ is the final...
Hello, you can call me V! I just got into highschool and am interested in physics, but I am super bad at math and science... I've been an english and art person my whole life so it's been tough LOL. I joined in the hopes that surrounding myself with STEM related stuff will have a positive...
Hello everyone,
I am very new to the concept of advanced math and am looking to broaden my knowledge.
I had sort of a vision involving the concept of swirling water and it has led me down the path of rotational energy. I am eager to learn
more and contribute if possible in the future to the...
Do papers done without the math get approved? I've got some ideas about how the universe works but I've just focused on intuitively understanding how GR works and never got interested in the math end until now that I'm finished. Or should I just focus on that part now?
Hello everyone .
Recently i have been thinking about the importance of math in physics . There are many times that i read books or papers that contain tons of hard math and yet i feel it doesn't really add that much to my understanding . On the other hand there are sources that provide a very...
Would a professor in a linear algebra, another upper-level math course, or an upper-level physics course take off points if I don't show steps when factoring an equation expression?
Hi everyone, I'm fibrebundle. I actually joined this forum because I'm really interested in abstract maths. I'm particularly intereseted in alegebraic topology and geometry at the moment. But I'm also really interested in spectral graph and graph theory. I'm starting grad school in engineering...
I'm an undergrad physics and computer science student most of the way done with my degrees. I have a background in math (calculus, linear algebra, a little bit of group theory). Machine learning and data science are also areas that I'm actively studying. For anyone interested, my name is based...
I'm a teenager eager to learn more about math and physics. As a self-directed learner, I'm particularly interested in calculus and linear algebra. I'm thrilled to be part of this community and look forward to gaining knowledge and engaging in enriching discussions. Your expertise and insights...
Let ##\gamma > 1##. If ##(X,d)## is a metric space and ##f : \mathbb{R} \to X## satisfies ##d(f(x),f(y)) \le |x - y|^\gamma## for all ##x,y\in \mathbb{R}##, show that ##f## must be constant.